Valuation equilibrium with crubs

This paper considers model worlds in which there are a continuum of individuaIs who form finite sized associations to undertake joint activities. We show that if there are a finite set of types and the commodity space contains lotteries, then the c1assicaI equilibrium results on convex economies can be reinterpreted to apply. Furthermore, in this lottery economy deterministic aIlocations (that is, degenerate lotteries) are generally not Pareto optimal, nor are they equilibria. In the interests of making the model seem more "natural," we show that the set of equilibria in a decentraIization in which individuaIs first gamble over vaIue transfers and then trade commodities in a deterministic competitive market economy are equivalent to those of our competi tive economy with a lottery commodity space.

Equilibria in exchange economies with financial constraints : beyond the Cass trick

We consider an exchange economy under incomplete financiaI markets with purely financiaI securities and finitely many agents. When portfolios are not constrained, Cass [4], Duffie [7] and Florenzano-Gourdel [12] proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass [4] in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financiaI market is constrained by convex restrictions, provided that financiaI markets are collectively frictionless.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Prevalência de oclusopatias e caracteríticas cefalométricas e dentais de escolares cearense da cidade de Fortaleza

The people of Ceará state are descended from miscegenation between the Portuguese colonizers and the native population, resulting in a different facial pattern from other populations. It is important that this pattern be thoroughly understood, along with its minimum and maximum values so that they can be assessed and respected, allowing professionals who deal with the craniofacial complex to work more efficiently and scientifically. Aim: To characterize the morphological pattern of individuals from Ceará state, whose father and grandfather are also native from Ceará, in the 10-12 year age group, not submitted to previous orthodontic treatment, in order to determine: 1) the prevalence of occlusal pattern; 2) the prevalence of dental anomalies (DA) and, 3) the skeletal and dental cephalometric characteristics of individuals that present with normal occlusion and harmonious facial pattern. Methodology: A list of 10-12 year-olds was obtained from 515 schools containing 162,713 students (Education Secretariat of Ceará State), from which 234 individuals were examined (107 boys and 157 girls). The assessment criteria adopted were: 1) Angle s Classification System to determine occlusal pattern. The occlusal characteristics were measured through overbite, overjet, crowding and interincisal diastema. 2) DA are anomalies of number, shape, size, eruption and structure and, 3) in the group that presented with normal occlusion, we used cephalometric analysis measures proposed by Downs, Steiner, Tweed, Holdaway, Jacobson and McNamara. Results: 1) 25.8% of the schoolchildren had normal occlusion, 47.5% class I malocclusion, 22.3% class II malocclusion and 4.2% class III malocclusion. No statistically significant difference was found between the age group studied and sex. Thirty percent of the individuals had normal overbite, while 36.7% and 19.7% had increased and reduced overbite, respectively. Normal overjet was found in 33.7% of the individuals, increased overjet in 50% and reduced in 16.3%. Dental crowding was observed in 62.5% of the individuals and the presence of interincisal diastema in 14.8%. 2) The prevalence of DA was 56.1%, 6.8% in the number, 10.8% in shape, 4.1% in size, 34.5% in eruption, 26.4% in structure and 17.4% had more than one DA. No association was found between DA and sex, but DA was significantly associated to malocclusion (p<0.05); 3) there was no association between sex or facial type between the measures of nasal-labial angle, position and effective maxillary length, effective mandibular length and the sagittal relationship between the molars, overjet and overbite, position of upper incisors, lower incisors and between the incisors themselves. There was a difference between sex, on the VERT index and in lower anterior facial height, upper incisor inclination and line-H, between facial types for the occlusal plane angles, mandibular plane, facial axis, lower incisor inclination, mandibular position, upper incisor position, lower anterior facial height, ANB and line-H. It was concluded that: 1) the most prevalent occlusal type was class I malocclusion, with no distinction for sex or age group, and the assessment of occlusal characteristics showed that excessive overbite and overjet were the most predominant findings, along with a high occurrence of tooth crowding; 2) a high prevalence of DA was found, particularly eruption anomalies, not influenced by sex but significantly associated to malocclusion and 3) individuals from Ceará are predominantly brachyfacial, exhibiting a number of similarities inherent to their facial pattern, such as a convex profile, retracted jaw, reduced lower third and protruded lower incisors. This study was multidisciplinary, involving researchers from the areas of epidemiology, radiology and dentistry, thereby meeting the multidisciplinarity requirements of the Postgraduate Program in Health Sciences

Variabilidade espacial de atributos químicos de um argissolo para aplicação de insumos à taxa variável em diferentes formas de relevo

A agricultura de precisão implica análise da variabilidade espacial de fatores de produção e a aplicação de insumos de forma localizada. Várias são as causas que condicionam a variabilidade espacial dos solos, sendo o relevo um dos fatores mais importantes. O presente estudo teve por objetivo analisar a variabilidade espacial dos atributos químicos do solo e a elaboração de mapas de necessidade de aplicação de insumos de forma localizada, em áreas com diferentes formas de relevo. Duas parcelas de 1 ha cada foram delimitadas em áreas com topografia côncava e convexa. Foram retiradas, em cada área, 242 amostras de solos em 121 pontos, nas profundidades de solo de 0,00-0,20 m e 0,20-0,40 m. Os resultados de análise química foram submetidos às análises da estatística descritiva, geoestatística e interpolação por krigagem. A área convexa apresentou maior variabilidade espacial do solo em relação a área côncava. A adoção da agricultura de precisão possibilitou economia de aproximadamente 25 kg ha-1 de P2O5 na área côncava.

Spatial variability of physical attributes of an alfisol under different hillslope curvatures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mapeamento das formas do relevo para estimativa de custos de fertilização em cana-de-açúcar

A modelagem matemática associada ao conhecimento da variabilidade dos atributos do solo e mapeamento das formas do relevo pode auxiliar no manejo da fertilidade do solo em usinas sucroalcooleiras. O presente trabalho teve como objetivo avaliar o uso da geoestatística e da modelagem matemática na estimativa de custos de fertilização, em diferentes formas do relevo. em uma área de 200 ha, foram identificadas duas formas de relevo, uma côncava e outra convexa, sendo os solos coletados nos pontos de cruzamento de uma malha, com intervalos regulares de 50 m, perfazendo um total de 623 pontos. As amostras foram submetidas a análises químicas, e, posteriormente, os dados foram avaliados por meio da estatística descritiva, geoestatística e modelagem matemática. Os resultados mostraram que, quando as formas do relevo são incorporadas às análises geoestatística e de modelagem matemática, ocorre aumento na eficiência de aplicação do calcário, fósforo e potássio no solo.

Variabilidade espacial de atributos mineralógicos de um latossolo sob diferentes formas do relevo: I - mineralogia da fração argila

A distribuição dos minerais da fração argila depende de condições pedoambientais específicas. O estudo das relações entre atributos desses minerais e locais específicos de sua ocorrência na paisagem torna-se importante para o entendimento das relações entre a mineralogia e os demais atributos do solo. Este trabalho teve como objetivo avaliar os atributos cristalográficos, as razões Gt/(Gt+Hm) e Ct/(Ct+Gb) dos minerais da fração argila (hematita, goethita, caulinita e gibbsita) e o padrão de distribuição espacial destes em um Latossolo Vermelho eutroférrico sob cultivo de cana-de-açúcar há mais de 30 anos, com colheita no sistema cana crua. As amostras de solo foram coletadas nos pontos de cruzamento de uma malha, georreferenciados, com intervalos regulares de 10 m, e dimensão de 100 x 100 m, na profundidade de 0,2-0,4 m, totalizando 119 pontos, em uma área de 1 ha. As amostras de solos foram analisadas quimicamente. Posteriormente, a fração argila foi submetida à difração de raios X. Foram feitas as análises estatísticas e geoestatísticas dos atributos cristalográficos dos minerais analisados. Mapas de krigagem foram realizados para a visualização da variabilidade espacial dos atributos. Todos os atributos estudados apresentaram dependência espacial, e os atributos mineralógicos apresentaram-se relacionados com variações das formas do relevo. A gibbsita apresentou o maior diâmetro médio do cristal (DMC) entre os minerais da fração argila estudados, e a goethita foi o mineral que apresentou a maior variação do DMC e da largura à meia altura. Os maiores valores do DMC da goethita, hematita e gibbsita foram encontrados no compartimento II, caracterizado por uma área côncavo-convexa.

Mineralogy of the clay fraction of Alfisols in two slope curvatures: III - spatial variability

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Small relief shape variations influence spatial variability of soil chemical attributes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hillslope curvature, clay mineralogy, and phosphorus adsorption in an Alfisol cultivated with sugarcane

As curvaturas do relevo promovem pedoambientes específicos que condicionam os atributos químicos e mineralógicos do solo e podem auxiliar na definição de zonas específicas de manejo. O fósforo (P) é um dos principais elementos limitantes ao desenvolvimento e longevidade do canavial. O teor e a constituição mineralógica da fração argila assumem papel importante na disponibilidade do P, sendo que a gibbsita (Gb), quando presente em altas proporções no solo, pode ser a principal responsável pela sua adsorção e indisponibilidade. Investigaram-se as relações e a variabilidade espacial da adsorção de P e a ocorrência de caulinita (Ct) e gibbsita na fração argila de um Argissolo Vermelho-Amarelo eutrófico originado de rochas areníticas sob diferentes curvaturas do relevo em área sob cultivo de cana-de-açúcar. Duas malhas de 1 ha foram delimitadas numa área côncava e outra área convexa. Foram coletadas 121 amostras em cada área para realização das análises granulométricas, químicas e mineralógicas. A capacidade máxima de adsorção de P foi obtida em seis amostras escolhidas ao acaso em cada área. Os resultados foram submetidos às análises estatísticas descritiva e geoestatística. Os menores valores médios de P disponível encontraram-se na área convexa. Nesta área, a proporção de gibbsita, expressa pelos valores da razão [Gb/(Gb+Ct)] e os valores de capacidade máxima de adsorção de fósforo foram maiores do que na área côncava.

Caracterização mineralógica de Latossolos em diferentes feições do relevo na região de Jaboticabal, SP

Different surface land form expressed by the relief can cause variations in soil properties in different magnitudes, depending mainly on a specific location in the landscape. Therefore, the objective of this study was to make the mineralogical characterization of Oxisols in different relief forms in the region of Jaboticabal, SP. Three trenches were opened in the convex, linear and concave landforms, done morphological description of the soil horizons and collected soil samples for physical, chemical and mineralogical characterization. It was found that the oxidic mineralogy is dependent on the type of landform, with the dominance of goethite on the concave landform and hematite on the linear landform. The desferrific clay minerals exhibited dominance of gibbsite in the concave, compared to convex and linear landforms that were dominated by the kaolinitic mineralogy.

Classificação numérica e modelo digital de elevação na caracterização espacial de atributos dos solos

One of needs of modern agriculture is the prediction of spatial variability of soil properties at more detailed scales for sustainable management and optimization of management practices. The mathematical model associated with knowledge of variability of soil attributes and mapping of relief forms has helped in agricultural planning. In this regard the aim of this study was to characterize the spatial variability of physical and chemical properties of Oxisols and Ultisols using numerical classification and the digital elevation model. Two distinct landforms: convex for the Oxisol (158 ha) and linear for the Ultisol (172 ha). 53 samples from the Oxisol and 57 samples from the Ultisol were taken. Multivariate analysis of clusters of attributes studied from their euclidean distances was performed. This analysis by dendograms along with digital elevation models for different soils characterized was more homogeneous in Ultisol groups, and less homogeneous for the Oxisol in convex landform. These quantitative methods showed that the landforms conditioned the spatial pattern of soil attributes.